All you've shown is that they violated the Constitution before the McCarthy era. I already knew that. They violated the Constitution with the "In God We Trust" BS on some of the the coins from time to time; then during the McCarthy era, they decided to violate the Constitution on all the money, not just on some of it.

The historian makes it clear what their motivation was:

This was right after the McCarthy era, during the early Cold War, when no congressperson would dare be seen voting against "God."

The connection to McCarthyist paranoia is clear; you just choose to ignore it. Just because you're capable of ignoring it, doesn't change the history.